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PubMed2004

Density functional theory of fluids in the isothermal-isobaric ensemble.

We present a density functional theory for inhomogeneous fluids at constant external pressure. The theory is formulated for a volume-dependent density, n(r,V), defined as the conjugate variable of a generalized external potential, nu(r,V), that conveys the information on the pressure. An exact expression for the isothermal-isobaric free-energy density functional is obtained in terms of the corresponding canonical ensemble functional. As an application we consider a hard-sphere system in a spherical pore with fluctuating radius. In general we obtain very good agreement with simulation. However, in some situations a peak develops in the center of the cavity and the agreement between theory and simulation becomes worse. This happens for systems where the number of particles is close to the magic numbers N=13, 55, and 147.

Journal Article↗

PubMed2004

An application of flexible constraints in Monte Carlo simulations of the isobaric--isothermal ensemble of liquid water and ice Ih with the polarizable and flexible mobile charge densities in harmonic oscillators model.

The method of flexible constraints was implemented in a Monte Carlo code to perform numerical simulations of liquid water and ice Ih in the constant number of molecules, volume, and temperature and constant pressure, instead of volume ensembles, using the polarizable and flexible mobile charge densities in harmonic oscillators (MCDHO) model. The structural and energetic results for the liquid at T=298 K and rho=997 kg m(-3) were in good agreement with those obtained from molecular dynamics. The density obtained at P=1 atm with flexible constraints, rho=1008 kg m(-3), was slightly lower than with the classical sampling of the intramolecular vibrations, rho=1010 kg m(-3). The comparison of the structures and energies found for water hexamers and for ice Ih with six standard empirical models to those obtained with MCDHO, show this latter to perform better in describing water far from ambient conditions: the MCDHO minimum lattice energy, density, and lattice constants were in good agreement with experiment. The average angle HOH of the water molecule in ice was predicted to be slightly larger than in the liquid, yet 1.2% smaller than the experimental value.

Journal Article↗

PubMed2004

Single-ensemble nonequilibrium path-sampling estimates of free energy differences.

We introduce a straightforward, single-ensemble, path sampling approach to calculate free energy differences based on Jarzynski's relation. For a two-dimensional "toy" test system, the new (minimally optimized) method performs roughly one hundred times faster than either optimized "traditional" Jarzynski calculations or conventional thermodynamic integration. The simplicity of the underlying formalism suggests the approach will find broad applicability in molecular systems.

Biopolymers↗

PubMed2004

Interatomic Lennard-Jones potentials of linear and branched alkanes calibrated by Gibbs ensemble simulations for vapor-liquid equilibria.

We propose Lennard-Jones potential parameters for interatomic interactions of linear and branched alkanes based on matching the results of Gibbs ensemble simulations of vapor-liquid equilibria to experimental data. The alkane model is similar as in the OPLS-AA, but multiple atom types for carbon based on the number of covalently bonded hydrogen atoms are necessary to accurately reproduce liquid densities and enthalpies of vaporization with the errors of 2.1% and 3.3%, respectively, for hydrocarbons of various chain lengths and structures. We find that the attraction energies of the carbon atoms are almost proportional to the number of covalent hydrogen atoms with each increasing the carbon energy parameter by approximately 0.033 kcal/mol. Though the present force field outperforms the OPLS-AA force field for alkanes we studied, systematic deviations for vapor pressures are still observed with errors of 15%-30%, and critical temperatures are slightly underestimated. We think that these shortcomings are probably due to the inadequacy of the two-parameter Lennard-Jones potential, and especially its behavior at short distances.

Journal Article↗

PubMed2004

Selection rules for probing biexcitons and electron spin transitions in isotropic quantum dot ensembles.

Three-dimensional rotational averages are evaluated for third-order nonlinear spectroscopic measurements of quantum dots. Photon echo, transient grating, and transient absorption are explicitly considered. It is shown that (a) biexciton formation can be suppressed relative to other contributions to nonlinear spectroscopies for isotropic nanocrystal ensembles by choice of polarizations for the excitation pulses; (b) circularly polarized excitation light can differentiate between exciton spin states in nonlinear optical experiments; and (c) electron spin state flip kinetics can be probed directly in an isotropic quantum dot system by using certain sequences of linear cross-polarized pulses.

Journal Article↗

PubMed2005

Isomolar semigrand ensemble molecular dynamics: development and application to liquid-liquid equilibria.

An extended system molecular dynamics method for the isomolar semigrand ensemble (fixed number of particles, pressure, temperature, and fugacity fraction) is developed and applied to the calculation of liquid-liquid equilibria (LLE) for two Lennard-Jones mixtures. The method utilizes an extended system variable to dynamically control the fugacity fraction xi of the mixture by gradually transforming the identity of particles in the system. Two approaches are used to compute coexistence points. The first approach uses multiple-histogram reweighting techniques to determine the coexistence xi and compositions of each phase at temperatures near the upper critical solution temperature. The second approach, useful for cases in which there is no critical solution temperature, is based on principles of small system thermodynamics. In this case a coexistence point is found by running N-P-T-xi simulations at a common temperature and pressure and varying the fugacity fraction to map out the difference in chemical potential between the two species A and B (mu(A)-mu(B)) as a function of composition. Once this curve is known the equal-distance/equal-area criterion is used to determine the coexistence point. Both approaches give results that are comparable to those of previous Monte Carlo (MC) simulations. By formulating this approach in a molecular dynamics framework, it should be easier to compute the LLE of complex molecules whose intramolecular degrees of freedom are often difficult to properly sample with MC techniques.

Journal Article↗

PubMed2005

Dense orientationally ordered states of a single semiflexible macromolecule: an expanded ensemble Monte Carlo simulation.

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.

Journal Article↗

PubMed2005

Solvation of sodium-chloride ion pair in water cluster at atmospheric conditions: grand canonical ensemble Monte Carlo simulation.

Open statistical ensemble simulations are used to study the mechanism of nucleation of atmospheric water on sodium-chloride ion pair in a wide range of temperature and relative humidity values. The extended simple point-charge model is used for water molecules. Ions-water nonadditive interactions are taken into account by introducing the mutual polarization of ions and water in the field of each other. Gibbs free-energy variations are calculated from Na+-Cl- pair-correlation function and used as a criterion for determining the possible stable states of the cluster. In this relation, it was found that the dissociation of ion pairs in water clusters occurs even at vapor pressures of only a few millibars. In the conditions under consideration solvent-separated ion-pair states are found to be more probable than contact ion-pair configurations. The susceptibilities of water and ions are found to play an essential role in the stabilization of ions at large separations. The structure of ion-induced clusters is analyzed in terms of binary correlation functions. The non-pair interactions influence essentially the structure of ion solvation shells. The results of simulation show that the separation of the charges in water clusters containing simple ions can take place under atmospheric conditions.

Journal Article↗

PubMed2005

Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids.

We apply the recently developed adaptive ensemble optimization technique to simulate dense Lennard-Jones fluids and a particle-solvent model by broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is improved by sampling an optimized histogram in radial coordinates that shifts statistical weight towards the entropic barriers between the shells of the liquid. Interstitial states in the vicinity of these barriers are identified with unprecedented accuracy by sharp signatures in the quickly converging histogram and measurements of the local diffusivity. The radial distribution function and potential of mean force are calculated to high precision.

Journal Article↗

PubMed2006

On the use of transition matrix methods with extended ensembles.

Different extended ensemble schemes for non-Boltzmann sampling (NBS) of a selected reaction coordinate lambda were formulated so that they employ (i) "variable" sampling window schemes (that include the "successive umbrella sampling" method) to comprehensibly explore the lambda domain and (ii) transition matrix methods to iteratively obtain the underlying free-energy eta landscape (or "importance" weights) associated with lambda. The connection between "acceptance ratio" and transition matrix methods was first established to form the basis of the approach for estimating eta(lambda). The validity and performance of the different NBS schemes were then assessed using as lambda coordinate the configurational energy of the Lennard-Jones fluid. For the cases studied, it was found that the convergence rate in the estimation of eta is little affected by the use of data from high-order transitions, while it is noticeably improved by the use of a broader window of sampling in the variable window methods. Finally, it is shown how an "elastic" window of sampling can be used to effectively enact (nonuniform) preferential sampling over the lambda domain, and how to stitch the weights from separate one-dimensional NBS runs to produce a eta surface over a two-dimensional domain.

Journal Article↗

PubMed2006

On a new self-consistent-field theory for the canonical ensemble.

A significant amount of many-body problems of quantum or classical equilibrium statistical mechanics are conveniently treated at fixed temperature and system size. In this paper, we present a new functional integral approach for solving canonical ensemble problems over the entire coupling range, relying on the method of Gaussian equivalent representation of Efimov and Ganbold. We demonstrate its suitability and competitiveness for performing approximate calculations of thermodynamic and structural quantities on the example of a repulsive potential model, widely used in soft matter theory.

Journal Article↗

PubMed2006

Gibbs ensemble Monte Carlo simulation of supercritical CO2 adsorption on NaA and NaX zeolites.

Adsorption of supercritical carbon dioxide on two kinds of zeolites with identical chemical composition but different pore structure (NaA and NaX) was studied using the Gibbs ensemble Monte Carlo simulation. The model frameworks for the two zeolites with SiAl ratio being unity have been chosen as the solid structures in the simulation. The adsorption behaviors of supercritical CO2 on the NaA and NaX zeolites, based on the adsorption isotherms and isosteric heats of adsorption, were discussed in detail and were compared with the available experimental results. A good agreement between the simulated and experimental results is obtained for both the adsorbed amount and the bulk phase density. The intermediate configurational snapshots and the radial distribution functions between zeolite and adsorbed CO2 molecules were collected in order to investigate the preferable adsorption locations and the confined structure behavior of CO2. The structure behaviors of the adsorbed CO2 molecules show various performances, as compared with the bulk phase, due to the confined effect in the zeolite pores.

Journal Article↗

PubMed2006

All-atom multiscaling and new ensembles for dynamical nanoparticles.

Viruses and other nanoparticles have mixed microscopic/macroscopic character. Thus it is natural to develop an understanding of their dynamics via a multiscale analysis of the Liouville equation following prescriptions introduced for the study of Brownian motion. However, the internal dynamics of the atoms constituting a nanoparticle introduces conceptual and technical difficulties associated with a description involving both the atomistic and nanometer scale properties of these systems and the potential overcounting of degrees of freedom. To overcome these difficulties we introduce a "nanocanonical" ensemble method to facilitate the multiscale analysis of the all-atom Liouville equation. Our approach overcomes technical difficulties associated with the removal of secular behavior, which leads to Fokker-Planck-type equations. Our approach ensures removal of all secular behavior in the N-atom probability density and not just that of a reduced distribution. Being based on a calibrated interatomic force field, our method has the potential to yield parameter-free universal models for nanoparticle dynamics including viral migration in complex media and viral phase transitions and disassembly.

Chemistry, Physical↗

PubMed2006

The Jarzynski identity derived from general Hamiltonian or non-Hamiltonian dynamics reproducing NVT or NPT ensembles.

The Jarzynski identity (JI) relates nonequilibrium work averages to thermodynamic free energy differences. It was shown in a recent contribution [M. A. Cuendet, Phys. Rev. Lett. 96, 120602 (2006)] that the JI can, in particular, be derived directly from the Nose-Hoover thermostated dynamics. This statistical mechanical derivation is particularly relevant in the framework of molecular dynamics simulation, because it is based solely on the equations of motion considered and is free of any additional assumptions on system size or bath coupling. Here, this result is generalized to a variety of dynamics, along two directions. On the one hand, specific improved thermostating schemes used in practical applications are treated. These include Nose-Hoover chains, higher moment thermostats, as well as an isothermal-isobaric scheme yielding the JI in the NPT ensemble. On the other hand, the theoretical generality of the new derivation is explored. Generic dynamics with arbitrary coupling terms and an arbitrary number of thermostating variables, both non-Hamiltonian and Hamiltonian, are shown to imply the JI. In particular, a nonautonomous formulation of the generalized Nose-Poincare thermostat is proposed. Finally, general conditions required for the JI derivation are briefly discussed.

Models, Chemical↗

PubMed2006

Molecular grand-canonical ensemble density functional theory and exploration of chemical space.

We present a rigorous description of chemical space within a molecular grand-canonical ensemble multi-component density functional theory framework. A total energy density functional for chemical compounds in contact with an electron and a proton bath is introduced using Lagrange multipliers which correspond to the energetic response to changes of the elementary particle densities. From a generalized Gibbs-Duhem equation analog, reactivity indices such as the nuclear hardness and a molecular Fukui function, which couples the grand-canonical electronic and nuclear degrees of freedom, are obtained. Maxwell relations between composition particles, ionic displacements, and the external potential are discussed. Numerical results for the molecular Fukui function are presented as well as finite temperature estimates for the oxidation of ammonia.

Journal Article↗

PubMed2006

A density functional theory study of the dissociation of H2 on gold clusters: importance of fluxionality and ensemble effects.

Density functional theory was employed to calculate the adsorption/dissociation of H2 on gold surfaces, Au(111) and Au(100), and on gold particles from 0.7 (Au14) to 1.2 nm (Au29). Flat surfaces of the bulk metal were not active towards H2, but a different effect was observed in gold nanoclusters, where the hydrogen was adsorbed through a dissociative pathway. Several parameters such as the coordination of the Au atoms, ensemble effects and fluxionality of the particle were analyzed to explain the observed activity. The effect of the employed functional was also studied. The flexibility of the structure, i.e., its adaptability towards the adsorbate, plays a key role in the bonding and dissociation of H2. The interaction with hydrogen leads to drastic changes in the structure of the Au nanoparticles. Furthermore, it appears that not only low coordinated Au atoms are needed because H2 adsorption/dissociation was only observed when a cooperation between several (4) active Au atoms was allowed.

Journal Article↗

PubMed2006

Isomolar-semigrand ensemble molecular dynamics: application to vapor-liquid equilibrium of the mixture methane/ethane.

The isomolar-semigrand ensemble molecular dynamics (iSGMD) method is applied to the simulation of the binary system methane/ethane. The vapor-liquid equilibrium properties of this system at a temperature of 192.37 K are computed using the Gibbs-Duhem integration method. The iSGMD method, which resembles conventional hybrid Monte Carlo (MC) but is applicable to phase equilibrium calculations, is designed to overcome the difficulties associated with performing standard Monte Carlo-type particle transformations in liquid systems that are very dense and/or are comprised of complex molecules with many intramolecular degrees of freedom. This work shows that particle transformations using the iSGMD method for the simple system methane/ethane are at least 25 times more successful than standard MC-type transformations. The P-x-y curve for the system methane/ethane at 192.37 K computed using iSGMD simulations agrees very well with the experimental P-x-y curve as well as results of a previous MC study.

Journal Article↗

PubMed2004

Learning modulates the ensemble representations for odors in primary olfactory networks.

Recent evidence suggests that odor-driven responses in the insect antennal lobe (AL) can be modified by associative and nonassociative processes, as has been shown in the vertebrate olfactory bulb. However, the specific network changes that occur in response to olfactory learning remain unknown. To characterize changes in AL network activity during learning, we developed an in vivo protocol in Manduca sexta that allows continuous monitoring of neural ensembles and feeding behavior over the course of olfactory conditioning. Here, we show that Pavlovian conditioning produced a net recruitment of responsive neural units across the AL that persisted after conditioning. Recruitment only occurred when odor reliably predicted food. Conversely, when odor did not predict food, a net loss of responsive units occurred. Simultaneous measures of feeding responses indicated that the treatment-specific patterns of neural recruitment were positively correlated with changes in the insect's behavioral response to odor. In addition to recruitment, conditioning also produced consistent and profound shifts in the temporal responses of 16% of recorded units. These results show that odor representations in the AL are dynamic and related to olfactory memory consolidation. We furthermore provide evidence that the basis of the learning-dependent changes in the AL is not simply an increase in activity in the neural network representing an odorant. Rather, learning produces a restructuring of spatial and temporal components of network responses to odor in the AL.

Animals↗